1. Field of the Invention
The present invention relates to computer aided design (CAD) of integrated circuits, and more specifically to a method and apparatus for determining electro_migration (EM) and/or voltage (IR) drop in integrated circuit designs.
2. Related Art
The designs of integrated circuits (ICs) are often represented in digital format, and analyzed for conformance with various requirements. Typically, designs are analyzed prior to fabrication of corresponding integrated circuits. By ensuring that the design conforms to various requirements prior to fabrication, unneeded time delays and cost overruns may be avoided, as is well known in the relevant arts.
One of the tasks in such circuit design analysis is electro-migration (EM) migration. EM generally refers to dislodging of ions from a metal wire (connecting nodes in an IC), and is caused by current density (current flow divided by width of the metal) exceeding a corresponding threshold. EM impedes the ability of metal to conduct, in addition to leading to reduced life-time. Accordingly, it is generally desirable to ensure that current density not exceed a desired threshold at least for a substantial amount. Thus, it may be desirable to ensure that an IC design be analyzed for EM migration.
Another task of interest in circuit design analysis is voltage drop analysis. Voltage (or IR) drop generally refers to a difference of a voltage level from a supply voltage (e.g., Vdd) at a node of interest and is usually caused by the resistance (either due to parasitic resistance or due to other components in the path) present between a voltage source (providing the supply voltage) and the node of interest.
As a result, circuit component(s) which are connected to nodes (other than the supply voltage nodes) may receive a terminal voltage, which is lesser than the supply voltage. If the terminal voltage is lesser than a corresponding permissible threshold, the circuit components may not operate in an desired manner. For example, a circuit may become non-operational or operate at a lower frequency (compared to a desired optimal frequency). Accordingly, it may be desirable to perform voltage drop analysis to ensure that various nodes of interest receive at least corresponding threshold voltages.
Analysis of circuit designs needs to be performed while taking into account various considerations. In general, it is desirable that various tasks be performed with at least some desired level of accuracy without consuming substantial time (or number of computations).
In the drawings, like reference numbers generally indicate identical, functionally similar, and/or structurally similar elements. The drawing in which an element first appears is indicated by the leftmost digit(s) in the corresponding reference number.